Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

Request Permissions   Purchase Content 
 

 

Operator synthesis and tensor products


Authors: G. K. Eleftherakis and I. G. Todorov
Journal: Trans. Amer. Math. Soc. 368 (2016), 5271-5300
MSC (2010): Primary 46A32; Secondary 47L35, 47L05
DOI: https://doi.org/10.1090/tran/6536
Published electronically: October 29, 2015
MathSciNet review: 3458381
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We show that Kraus' property $ S_{\sigma }$ is preserved under taking weak* closed sums with masa-bimodules of finite width and establish an intersection formula for weak* closed spans of tensor products, one of whose terms is a masa-bimodule of finite width. We initiate the study of the question of when operator synthesis is preserved under the formation of products and prove that the union of finitely many sets of the form $ \kappa \times \lambda $, where $ \kappa $ is a set of finite width while $ \lambda $ is operator synthetic, is, under a necessary restriction on the sets $ \lambda $, again operator synthetic. We show that property $ S_{\sigma }$ is preserved under spatial Morita subordinance.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 46A32, 47L35, 47L05

Retrieve articles in all journals with MSC (2010): 46A32, 47L35, 47L05


Additional Information

G. K. Eleftherakis
Affiliation: Department of Mathematics, Faculty of Sciences, University of Patras, 265 00 Patras, Greece
Email: gelefth@math.upatras.gr

I. G. Todorov
Affiliation: Pure Mathematics Research Centre, Queen’s University Belfast, Belfast BT7 1NN, United Kingdom
Email: i.todorov@qub.ac.uk

DOI: https://doi.org/10.1090/tran/6536
Received by editor(s): February 5, 2013
Received by editor(s) in revised form: February 21, 2013, and May 20, 2014
Published electronically: October 29, 2015
Article copyright: © Copyright 2015 American Mathematical Society